Deep Implicit Functions (DIFs) have gained popularity in 3D computer vision due to their compactness and continuous representation capabilities. However, addressing dense correspondences and semantic relationships across DIF-encoded shapes remains a critical challenge, limiting their applications in texture transfer and shape analysis. Moreover, recent endeavors in 3D shape generation using DIFs often neglect correspondence and topology preservation. This paper presents HNDF (Hybrid Neural Diffeomorphic Flow), a method that implicitly learns the underlying representation and decomposes intricate dense correspondences into explicitly axis-aligned triplane features. To avoid suboptimal representations trapped in local minima, we propose hybrid supervision that captures both local and global correspondences. Unlike conventional approaches that directly generate new 3D shapes, we further explore the idea of shape generation with deformed template shape via diffeomorphic flows, where the deformation is encoded by the generated triplane features. Leveraging a pre-existing 2D diffusion model, we produce high-quality and diverse 3D diffeomorphic flows through generated triplanes features, ensuring topological consistency with the template shape. Extensive experiments on medical image organ segmentation datasets evaluate the effectiveness of HNDF in 3D shape representation and generation.

本文介绍了一种新的神经网络模型HNDF (Hybrid Neural Diffeomorphic Flow)，用于三维形状重建和生成，通过学习数据样本中的隐式函数，对细节信息进行拆分和处理，进一步实现高质量的三维形状再现和生成。

基于三平面的混合神经变形流形用于形状表示和生成